题文
答案
据专家权威分析，试题“如图，△ABC是等边三角形，点D是BC边上任意一点，DE⊥AB于点E，DF⊥..”主要考查你对 等边三角形，解直角三角形 等考点的理解。关于这些考点的“档案”如下：
等边三角形解直角三角形
考点名称：等边三角形
性质：①等边三角形是锐角三角形，等边三角形的内角都相等，且均为60°。②等边三角形每条边上的中线、高线和所对角的平分线互相重合（三线合一）③等边三角形是轴对称图形，它有三条对称轴，对称轴是每条边上的中线、高线 或对角的平分线所在的直线。④等边三角形重心、内心、外心、垂心重合于一点，称为等边三角形的中心。（四心合一）⑤等边三角形内任意一点到三边的距离之和为定值(等于其高)
判定方法：①三边相等的三角形是等边三角形（定义）②三个内角都相等（为60度）的三角形是等边三角形③有一个角是60度的等腰三角形是等边三角形④ 两个内角为60度的三角形是等边三角形说明:可首先考虑判断三角形是等腰三角形。等边三角形的性质与判定理解：首先，明确等边三角形定义。三边相等的三角形叫做等边三角形，也称正三角形。其次，明确等边三角形与等腰三角形的关系。等边三角形是特殊的等腰三角形，等腰三角形不一定是等边三角形。
等比三角形的尺规做法：可以利用尺规作图的方式画出正三角形，其作法相当简单：先用尺画出一条任意长度的线段（这条线段的长度决定等边三角形的边长），再分别以线段二端点为圆心、线段为半径画圆，二圆汇交于二点，任选一点，和原来线段的两个端点画线段，则这二条线段和原来线段即构成一正三角形。
考点名称：解直角三角形
解直角三角形的函数值:
锐角三角函数：sinA=a/c,cosA=b/c,tanA=a/b,cotA=b/a（1）互余角的三角函数值之间的关系：若∠ A+∠ B=90°，那么sinA=cosB或sinB=cosA（2）同角的三角函数值之间的关系：①sin2A+cos2A=1②tanA=sinA/cosA③tanA=1/tanB④a/sinA=b/sinB=c/sinC（3）锐角三角函数随角度的变化规律：锐角∠A的tan值和sin值随着角度的增大而增大，cos值随着角度的增大而减小。
解直角三角形的函数值列举：sin1=0.01745240643728351 sin2=0.03489949670250097 sin3=0.05233595624294383 sin4=0.0697564737441253 sin5=0.08715574274765816 sin6=0.10452846326765346 sin7=0.12186934340514747 sin8=0.13917310096006544 sin9=0.15643446504023087 sin10=0.17364817766693033 sin11=0.1908089953765448 sin12=0.20791169081775931 sin13=0.22495105434386497 sin14=0.24192189559966773 sin15=0.25881904510252074 sin16=0.27563735581699916 sin17=0.2923717047227367 sin18=0.3090169943749474 sin19=0.3255681544571567 sin20=0.3420201433256687 sin21=0.35836794954530027 sin22=0.374606593415912 sin23=0.3907311284892737 sin24=0.40673664307580015 sin25=0.42261826174069944 sin26=0.4383711467890774 sin27=0.45399049973954675 sin28=0.4694715627858908 sin29=0.48480962024633706 sin30=0.49999999999999994 sin31=0.5150380749100542 sin32=0.5299192642332049 sin33=0.544639035015027 sin34=0.5591929034707468 sin35=0.573576436351046 sin36=0.5877852522924731 sin37=0.6018150231520483 sin38=0.6156614753256583 sin39=0.6293203910498375 sin40=0.6427876096865392 sin41=0.6560590289905073 sin42=0.6691306063588582 sin43=0.6819983600624985 sin44=0.6946583704589972 sin45=0.7071067811865475 sin46=0.7193398003386511 sin47=0.7313537016191705 sin48=0.7431448254773941 sin49=0.7547095802227719 sin50=0.766044443118978 sin51=0.7771459614569708 sin52=0.7880107536067219 sin53=0.7986355100472928 sin54=0.8090169943749474 sin55=0.8191520442889918 sin56=0.8290375725550417 sin57=0.8386705679454239 sin58=0.848048096156426 sin59=0.8571673007021122 sin60=0.8660254037844386 sin61=0.8746197071393957 sin62=0.8829475928589269 sin63=0.8910065241883678 sin64=0.898794046299167 sin65=0.9063077870366499 sin66=0.9135454576426009 sin67=0.9205048534524404 sin68=0.9271838545667873 sin69=0.9335804264972017 sin70=0.9396926207859083 sin71=0.9455185755993167 sin72=0.9510565162951535 sin73=0.9563047559630354 sin74=0.9612616959383189 sin75=0.9659258262890683 sin76=0.9702957262759965 sin77=0.9743700647852352 sin78=0.9781476007338057 sin79=0.981627183447664 sin80=0.984807753012208 sin81=0.9876883405951378 sin82=0.9902680687415704 sin83=0.992546151641322 sin84=0.9945218953682733 sin85=0.9961946980917455 sin86=0.9975640502598242 sin87=0.9986295347545738 sin88=0.9993908270190958 sin89=0.9998476951563913 sin90=1
cos1=0.9998476951563913 cos2=0.9993908270190958 cos3=0.9986295347545738 cos4=0.9975640502598242 cos5=0.9961946980917455 cos6=0.9945218953682733 cos7=0.992546151641322 cos8=0.9902680687415704 cos9=0.9876883405951378 cos10=0.984807753012208 cos11=0.981627183447664 cos12=0.9781476007338057 cos13=0.9743700647852352 cos14=0.9702957262759965 cos15=0.9659258262890683 cos16=0.9612616959383189 cos17=0.9563047559630355 cos18=0.9510565162951535 cos19=0.9455185755993168 cos20=0.9396926207859084 cos21=0.9335804264972017 cos22=0.9271838545667874 cos23=0.9205048534524404 cos24=0.9135454576426009 cos25=0.9063077870366499 cos26=0.898794046299167 cos27=0.8910065241883679 cos28=0.882947592858927 cos29=0.8746197071393957 cos30=0.8660254037844387 cos31=0.8571673007021123 cos32=0.848048096156426 cos33=0.838670567945424 cos34=0.8290375725550417 cos35=0.8191520442889918 cos36=0.8090169943749474 cos37=0.7986355100472928 cos38=0.7880107536067219 cos39=0.7771459614569709 cos40=0.766044443118978 cos41=0.754709580222772 cos42=0.7431448254773942 cos43=0.7313537016191705 cos44=0.7193398003386512 cos45=0.7071067811865476 cos46=0.6946583704589974 cos47=0.6819983600624985 cos48=0.6691306063588582 cos49=0.6560590289905074 cos50=0.6427876096865394 cos51=0.6293203910498375 cos52=0.6156614753256583 cos53=0.6018150231520484 cos54=0.5877852522924731 cos55=0.5735764363510462 cos56=0.5591929034707468 cos57=0.5446390350150272 cos58=0.5299192642332049 cos59=0.5150380749100544 cos60=0.5000000000000001 cos61=0.4848096202463371 cos62=0.46947156278589086 cos63=0.4539904997395468 cos64=0.43837114678907746 cos65=0.42261826174069944 cos66=0.4067366430758004 cos67=0.3907311284892737 cos68=0.3746065934159122 cos69=0.35836794954530015 cos70=0.3420201433256688 cos71=0.32556815445715675 cos72=0.30901699437494745 cos73=0.29237170472273677 cos74=0.27563735581699916 cos75=0.25881904510252074 cos76=0.24192189559966767 cos77=0.22495105434386514 cos78=0.20791169081775923 cos79=0.19080899537654491 cos80=0.17364817766693041 cos81=0.15643446504023092 cos82=0.13917310096006546 cos83=0.12186934340514749 cos84=0.10452846326765346 cos85=0.08715574274765836 cos86=0.06975647374412523 cos87=0.052335956242943966 cos88=0.03489949670250108 cos89=0.0174524064372836 cos90=0
tan1=0.017455064928217585 tan2=0.03492076949174773 tan3=0.052407779283041196 tan4=0.06992681194351041 tan5=0.08748866352592401 tan6=0.10510423526567646 tan7=0.1227845609029046 tan8=0.14054083470239145 tan9=0.15838444032453627 tan10=0.17632698070846497 tan11=0.19438030913771848 tan12=0.2125565616700221 tan13=0.2308681911255631 tan14=0.24932800284318068 tan15=0.2679491924311227 tan16=0.2867453857588079 tan17=0.30573068145866033 tan18=0.3249196962329063 tan19=0.34432761328966527 tan20=0.36397023426620234 tan21=0.3838640350354158 tan22=0.4040262258351568 tan23=0.4244748162096047 tan24=0.4452286853085361 tan25=0.4663076581549986 tan26=0.4877325885658614 tan27=0.5095254494944288 tan28=0.5317094316614788 tan29=0.554309051452769 tan30=0.5773502691896257 tan31=0.6008606190275604 tan32=0.6248693519093275 tan33=0.6494075931975104 tan34=0.6745085168424265 tan35=0.7002075382097097 tan36=0.7265425280053609 tan37=0.7535540501027942 tan38=0.7812856265067174 tan39=0.8097840331950072 tan40=0.8390996311772799 tan41=0.8692867378162267 tan42=0.9004040442978399 tan43=0.9325150861376618 tan44=0.9656887748070739 tan45=0.9999999999999999 tan46=1.0355303137905693 tan47=1.0723687100246826 tan48=1.1106125148291927 tan49=1.1503684072210092 tan50=1.19175359259421 tan51=1.234897156535051 tan52=1.2799416321930785 tan53=1.3270448216204098 tan54=1.3763819204711733 tan55=1.4281480067421144 tan56=1.4825609685127403 tan57=1.5398649638145827 tan58=1.6003345290410506 tan59=1.6642794823505173 tan60=1.7320508075688767 tan61=1.8040477552714235 tan62=1.8807264653463318 tan63=1.9626105055051503 tan64=2.050303841579296 tan65=2.1445069205095586 tan66=2.246036773904215 tan67=2.355852365823753 tan68=2.4750868534162946 tan69=2.6050890646938023 tan70=2.7474774194546216 tan71=2.904210877675822 tan72=3.0776835371752526 tan73=3.2708526184841404 tan74=3.4874144438409087 tan75=3.7320508075688776 tan76=4.0107809335358455 tan77=4.331475874284153 tan78=4.704630109478456 tan79=5.144554015970307 tan80=5.671281819617707 tan81=6.313751514675041 tan82=7.115369722384207 tan83=8.144346427974593 tan84=9.514364454222587 tan85=11.43005230276132 tan86=14.300666256711942 tan87=19.08113668772816 tan88=28.636253282915515 tan89=57.289961630759144 tan90=(无限)
（勾股定理）； 
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